Course Content
Class 9th Science
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Class 9th Math
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Class 9 Social Science History: India and the Contemporary World – I
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Class 9 Social Science Geography: Contemporary India – I
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Class 9 Social Science Civics (Political Science): Democratic Politics – I
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Class 9 Social Science Economics: Understanding Economic Development – I
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Class 9 English Beehive
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Class 9 English Beehive Poem
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Class 9 English Moments
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Online Class For 9th Standard Students (CBSE) (English Medium)

## Introduction of Lines And Angles Notes

Parallel lines with a transversal

• ∠1=∠5,∠2=∠6,∠4=∠8 and ∠3=∠7(Corresponding angles)
• ∠3=∠5,∠4=∠6 (Alternate interior angles)
• ∠1=∠7,∠2=∠8 (Alternate exterior angles)

Lines parallel to the same line

Lines that are parallel to the same line are also parallel to each other.

### Angles and types of angles

When 2 rays originate from the same point at different directions, they form an angle.

–    The rays are called arms and the common point is called the vertex
–    Types of angles : (i) Acute angle 0∘<a<90∘
(ii) Right angle a=90∘
(iii) Obtuse angle : 90∘<a<180∘
(iv) Straight angle =180∘
(v) Reflex Angle 180∘<a<360∘
(vi) Angles that add up to 90∘ are complementary angles
(vii) Angles that add up to 180∘ are called supplementary angles.

Intersecting Lines and Associated Angles

Intersecting and Non-Intersecting lines

• When 2 lines meet at a point they are called intersecting
• When 2 lines never meet at a point, they are called non-intersecting or parallel lines

2 angles are adjacent if they have the same vertex and one common point.

Linear Pair

When 2 adjacent angles are supplementary, i.e they form a straight line (add up to 180∘), they are called a linear pair.

Vertically opposite angles

When two lines intersect at a point, they form equal angles that are vertically opposite to each other.

### Basic Properties of a Triangle

Triangle and sum of its internal angles

Sum of all angles of a triangle add up to 180∘

An exterior angle of a triangle = sum of opposite internal angles

– If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles 